The Swedish frontman's close-range finish was enough to see off City at St. James' Park, with Eddie Howe's men richly deserving of their victory after a hugely improved second half display in front of their own supporters.
The win - Newcastle's third in four games - keeps their hopes in the competition well and truly alive as United bid to emulate last season's memorable run to the final.
A low key first half brought only a handful of attempts on goal, the majority of which were instigated by the visitors. Julian Alvarez forced Nick Pope into a save with his feet with the Newcastle backline required to be alert throughout. Paul Dummett's perfectly-timed sliding challenge to halt Jack Grealish's run through the middle showed the requisite level of attentiveness against such a potent side - and brought applause from Pep Guardiola too.
Josko Gvardiol saw a header blocked and Rico Lewis' effort from range took a nick on its way over the bar but perhaps the clearest opening of the half fell to Newcastle, against the run of play. Gvardiol's misplaced pass was intercepted by Joelinton and Isak's pass for Jacob Murphy on the right gave the winger a chance to put United in front. He couldn't find the right angle with his shot, though, as Stefan Ortega got down well to block it.
Two of the hosts' debutants, Lewis Miley and Lewis Hall, were replaced at the break by Bruno Guimarães and Anthony Gordon, and the changes immediately put Newcastle on the front foot. Seven minutes after the restart they had the lead; Murphy fed Joelinton, whose mazy run took him into the box and eventually just too wide for the Brazilian to get a shot away. But his low centre wasn't cut out by Lewis at the back post, leaving Isak the simple task of tapping home a goal that came as a deserved reward for their improvement at the start of the second period.
Only a timely Manuel Akanji challenge prevented Gordon from pulling the trigger soon after as Howe's men looked for another. Their illustrious opponents looked a shadow of the side they had been earlier on in the evening but they did try to turn the screw in the final 20 minutes. Grealish - well shackled by Tino Livramento for much of the contest - tried his luck from range, but Pope saved comfortably. A terrific intervention from Livramento then stopped City substitute Matheus Nunes as he homed in on goal.
The final exchanges weren't quite as nervy as might be expected when the Premier League champions are chasing a goal, however. Gordon saw a shot saved and at the other end, Nunes drove just wide. But this was Newcastle's night, exemplified by the excellent Dummett's thumping clearance - which was followed by another similarly uncompromising tackle from Matt Targett - in stoppage time as the hosts booked their place in the fourth round.
